Introduction to Fractals and Chaos

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Freely browse and use OCW materials at your own pace. There's no signup, and no start or end dates. Knowledge is your reward. Use OCW to guide your own life-long learning, or to teach others. What impact has chaos had, and what impact will it have in the future?

This is followed by a set of three appendices: a review of high school algebra, a discussion of histograms and distributions, and a guide to further reading. This last chapter deserves specific mention because it not only lists books but also discusses them, a feature I wish more textbooks would emulate.

Another noteworthy, and very attractive, feature of this chapter is that not only does it list journal articles, it contains a discussion of the peer-review process and offers suggestions to students as to how to search for articles. All numbers — complex and real — are imaginary. In addition to this overall conversational tone, the author makes frequent use of marginal notes to help clarify or explain points.

The book is also liberally sprinkled with photographs and pictures. Unfortunately, however, there are no color plates of the kind of beautiful fractal photographs that one typically finds in a book of this nature. This seems like an opportunity missed, but is hardly a critical defect, particularly since this is intended as a textbook, not a coffee table book. A lengthy solutions manual pages is available from the publisher.

All in all, this is a very valuable book.

Lecture - 14 Introduction to Fractals

This is an excellent book, and is highly recommended. Mark Hunacek mhunacek iastate. Introducing Discrete Dynamical Systems 0. Opening Remarks 1. Functions 2. Iterating Functions 3. Qualitative Dynamics 4. Time Series Plots 5. Graphical Iteration 6. Iterating Linear Functions 7. Population Models 8. Newton, Laplace, and Determinism II. Chaos 9. Chaos and the Logistic Equation The Buttery Effect The Bifurcation Diagram The final chapter of Part I is a nice digression on the nature of science and some of the controversy surrounding the question of what the assumption of a deterministic universe has to say about free will.

The logistic equation is a recurring example throughout these chapters, which also introduce the notion of bifurcation diagrams and some statistical concepts. Fractals are the subject of Part III of the text; they are introduced first by means of examples and then given a more precise definition.

The concept of fractal dimension is discussed at some length. In Part V, the author looks at types of dynamical systems other than the discretely-changing single-variable functions that were the focus of study to this point.

Encounters with Chaos and Fractals

This necessitates the introduction to the ideas of calculus that was previously mentioned, and which is applied to study such things as systems and phase planes, the Volterra prey-predator system, and the Lorenz equations. There is also a chapter on cellular automata, another kind of dynamical system. What impact has chaos had, and what impact will it have in the future? This is followed by a set of three appendices: a review of high school algebra, a discussion of histograms and distributions, and a guide to further reading.

This last chapter deserves specific mention because it not only lists books but also discusses them, a feature I wish more textbooks would emulate.


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Another noteworthy, and very attractive, feature of this chapter is that not only does it list journal articles, it contains a discussion of the peer-review process and offers suggestions to students as to how to search for articles. All numbers — complex and real — are imaginary. In addition to this overall conversational tone, the author makes frequent use of marginal notes to help clarify or explain points.

The book is also liberally sprinkled with photographs and pictures. Unfortunately, however, there are no color plates of the kind of beautiful fractal photographs that one typically finds in a book of this nature. This seems like an opportunity missed, but is hardly a critical defect, particularly since this is intended as a textbook, not a coffee table book. A lengthy solutions manual pages is available from the publisher.

Mathematics Courses

All in all, this is a very valuable book. This is an excellent book, and is highly recommended. Mark Hunacek mhunacek iastate. Introducing Discrete Dynamical Systems 0.

An Introduction to Fractals | Something of the Marvelous

Opening Remarks 1. Functions 2. Iterating Functions 3. Qualitative Dynamics 4. Time Series Plots 5. Graphical Iteration 6.

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